1. Vector Components

2. Addition of multiple vectors via the graphical solution is complexB E
It’s easier to use the mathematical method that will be described now

3. Mathematical Method
All vectors are placed on the origin of a Cartesian Coordinates System. Each Vector is replaced with it components X Y B C D A

4. The vector components of vector A are two perpendicular vectors Ax and Ay that are parallel to X and Y axis respectively, add their resultant vector is equal to A. y  x

5. Calculation of vector components
Module
Pythagoras
Note that the angle is not always marked relative to positive X axis direction Y θ X

6. Calculate vector A components
Example
Calculate vector A components x y

7. Vector representation depend on the chosen coordinate system (CS)
Vector representation depend on the chosen coordinate system (CS). Different CS does not change the vector, but only it’s representation x y  x’ y’  ax ay
ax’
ay’
The vector magnitude is independent of the CS, hence we have freedom to select the CS to ease the calculation

8. Vector addition, is done by adding the respective componentsβ θ X
Sum of the respective components yield the resultant vector components, hence we can find the resultant vector

9. Y β θ X

10. The unit vector is marked with a ^ sign above the letter
לסימן קוראים בשם "כובע" או "גג"

11. It is described by it’s components as any vector.
Unit vector is a vector the has a magnitude of 1 with no units, and has a direction
It is described by it’s components as any vector.

12. Representing a vector by it’s components is as follows:
The CS unit vectors are unit vectors pointing parallel to the X,Y and Z axes: x, y, z z y x
Representing a vector by it’s components is as follows:

13. Determine unit vector components of A
Draw the vector on the CS z
Determine a vector which is the same direction of vector A but has a magnitude of 1 y x

14. Magnitude of A z y x

15. Divide each component by the vector magnitude, results in a unit vector having same direction a vector A x y z

16. Check your understandingx y
3 cm A B
6 cm
450
Calculate:
The components of vectors A and B
The resultant vector components
The resultant vector magnitude and direction
Find the unit vector parallel to the resultant vector
A vector with magnitude 10 that is parallel to the resultant vector

17. The components of vectors A and B y B 6 cm
450 x
3 cm

18. The resultant vector components y B 6 cm
450 x
3 cm

19. The resultant vector magnitude and direction y
4.37
4.2
740 x
-1.2
Above Negative X Axis

20. Find the unit vector parallel to the resultant vector y
4.37
4.2
740 x
-1.2

21. A vector with magnitude 10 that is parallel to the resultant vector
Unit vector parallel to resultant vector

22. The End!